SOLUTION: A 50-foot ladder is placed at a 60-degree angle of elevation from the ground. The ladder terminates at the top of a building. a. Sketch the situation and label each side of the

Algebra ->  Trigonometry-basics -> SOLUTION: A 50-foot ladder is placed at a 60-degree angle of elevation from the ground. The ladder terminates at the top of a building. a. Sketch the situation and label each side of the       Log On


   

Question 1103340: A 50-foot ladder is placed at a 60-degree angle of elevation from the ground. The ladder terminates at the top of a building.
a. Sketch the situation and label each side of the triangle. H = height of the building,
L= length of ladder, D = distance between the bottom of the ladder and the bottom of the building. Identify which angle is the angle of elevation.
b. Use a trig function to calculate the distance between the bottom of the ladder
and the bottom of the building.
c. Use a trig function to calculate the height of the tower.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
yuur diagram will look something like this:

$$$

your angle of elevation is 60 degrees.

sin(60) = opposite / hypotenuse = H/L.

cos(60) = adjacent / hypotenuse = D/L.

since L = 50 (length of the ladder), then:

sin(60) = H/50.

cos(60) = D/50.

solve for H to get H = 50 * sin(60).

solve for D to get D = 50 * cos(60).

you will get H = 43.30127019

you will get D = 25

since you have a right triangle with a hypotenuse of L and two lets of H and D, then, by pythagorus, you should get L^2 = H^2 + D^2.

this becomes 50^2 = 43.30127019^2 + 25^2

solve to get 2500 = 1875 + 625 which becomes 2500 = 2500, confirming that the solution is correct.